{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 一维量子态传输"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "DeepQuantum 模拟一维简单量子态传输，通过给定的哈密顿量得到时间演化算符，对其进行特征值分解，得到对应的量子门，从而构造相应的量子线路进行求解。\n",
    "DeepQuantum 支持大规模的多比特模拟，通过设置mps=True可以使用张量网络求解。 \\\n",
    "考虑简单的N个比特一维链体系，给定的哈密顿量如下：$$H =\\sum_n\\sigma_n^x\\sigma_{n+1}^x$$ \\\n",
    "$\\sigma_n^x$ 代表作用在第n个比特的pauli x 算符，n取值为1,...,N-1。 \\\n",
    "因为哈密顿量中同时加入$\\sigma^x$和$\\sigma^y$时会出现不对易的情况，为了方便分解多比特的时间演化算符为多个两比特时间演化算符，此处只考虑$\\sigma^x_n \\cdot \\sigma^x_{n+1}$部分，因此是文献中的模型的简化(https://arxiv.org/pdf/quant-ph/0309131)。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import deepquantum as dq\n",
    "import torch\n",
    "import torch.nn as nn\n",
    "import numpy as np\n",
    "from numpy import linalg as la\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "首先考虑简单的两个比特情况，写出给定哈密顿量的矩阵形式，将时间演化算符进行特征值分解，得到由特征向量组成的矩阵u和对角矩阵u_diag，再通过自定义这两个量子门进行线路演化，最后对每个比特测量相应的概率。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_probs_(sigmaz_exp):\n",
    "    \"\"\"Obtain probs of |0> and |1> for each qubit\n",
    "    input: expectation values of sigmaz, type: torch.Tensor\n",
    "    output: prob for |0> and |1> for each qubit, size: (num_qubits, batch, 2)\n",
    "    \"\"\"\n",
    "    probs_all = torch.stack(((sigmaz_exp+1)/2, (1-sigmaz_exp)/2)).transpose(0,-1)\n",
    "\n",
    "    return probs_all"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "sigmax_d2 = np.matrix([[0, 1], [1, 0]])\n",
    "sigmax_d4 = np.kron(sigmax_d2, sigmax_d2)   # H\n",
    "u = la.eig(sigmax_d4)[1]                    # 特征值分解\n",
    "udag = u.transpose()\n",
    "eig_val = la.eig(sigmax_d4)[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 621.739x200.667 with 1 Axes>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# batch = 1\n",
    "nqubit = 2\n",
    "\n",
    "tlist = np.linspace(0, 2*np.pi, 100)\n",
    "probs_q0 = []\n",
    "probs_qend = []\n",
    "for i in range(100) :\n",
    "    t = tlist[i]\n",
    "\n",
    "    u_exp = np.diag(np.exp(eig_val*(-1j)*t))              # 构造对角矩阵Lambda\n",
    "\n",
    "    cir = dq.QubitCircuit(nqubit, mps=True, chi=2)        # mps=True 使用张量网络 \n",
    "    cir.x(0)                                              # initial state 10\n",
    "    cir.any(unitary=udag, wires=[0,1], name=\"udag_x\")     # u*exp(-i*Lambda*t)*u^dag\n",
    "    cir.any(unitary=u_exp, wires=[0,1], name=\"diag_t\")\n",
    "    cir.any(unitary=u, wires=[0,1], name=\"u_x\")\n",
    "\n",
    "\n",
    "    for i in range(nqubit):                               # sigmaz 平均值\n",
    "        cir.observable(i)\n",
    "    cir()\n",
    "\n",
    "    probs_q0.append((get_probs_(cir.expectation()).tolist())[0])\n",
    "    probs_qend.append((get_probs_(cir.expectation()).tolist())[1])\n",
    "\n",
    "cir.draw()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "probs_q0 = np.matrix(probs_q0)\n",
    "probs_qend = np.matrix(probs_qend)\n",
    "fig = plt.figure(figsize=(8, 5))\n",
    "ax = fig.add_subplot(111)\n",
    "plt.xlim(0, 2*np.pi)\n",
    "plt.ylim(-0.01, 1.01)\n",
    "plt.plot(tlist, probs_q0[:,1], label=\"$q_0=|1>$\", color=\"dodgerblue\")\n",
    "plt.plot(tlist, probs_qend[:,1], label=\"$q_1=|1>$\", color=\"red\")\n",
    "plt.vlines(np.pi/2, -0.1, 1.1, ls=\"--\")\n",
    "plt.text(1.6, 0.5, \"$t=\\pi/2$\")\n",
    "plt.xlabel(\"Time\")\n",
    "plt.ylabel(\"Probability\")\n",
    "plt.xticks([0, np.pi/2, np.pi, np.pi/2*3, 2*np.pi], \n",
    "           [0, \"$\\pi/2$\", \"$\\pi$\", \"$3\\pi/2$\", \"$2\\pi$\"]\n",
    "           )\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "对于多比特情况，哈密顿量的矩阵维度随比特数增多呈指数增长，但是容易证明其对应的时间演化算符特征值分解之后的结果可以写成张量积的形式，这说明时间演化算符可以分解成多个量子门的组合。下面给出任意多个比特的模拟，nqubit的值可以任意选择。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 2228.78x6973.17 with 1 Axes>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# batch = 1\n",
    "nqubit = 20\n",
    "\n",
    "tlist = np.linspace(0, 2*np.pi, 100)                     # time slicing \n",
    "allprobs_q0 = []\n",
    "allprobs_q1 = []\n",
    "allprobs_qend = []\n",
    "allprobs_qend2 = []\n",
    "for i in range(100) :\n",
    "    t = tlist[i]\n",
    "    cir = dq.QubitCircuit(nqubit, mps=True, chi=2)     # mps=True using Tensornetwork\n",
    "    cir.x(0)                                           # initial state 10\n",
    "     \n",
    "    for q in range(nqubit-1):\n",
    "        u_exp = np.diag(np.exp(eig_val*(-1j)*t))       # 构造对角矩阵Lambda        \n",
    "        cir.any(unitary=udag, wires=[q,q+1], name=\"udag_x\")  # u*exp(-i*Lambda*t)*u^dag\n",
    "        cir.any(unitary=u_exp, wires=[q,q+1], name=\"diag_t\")\n",
    "        cir.any(unitary=u, wires=[q,q+1], name=\"u_x\")\n",
    "\n",
    "    for i in range(nqubit):                             # sigmaz 平均值\n",
    "        cir.observable(i)\n",
    "    cir()\n",
    "\n",
    "    allprobs_q0.append((get_probs_(cir.expectation()).tolist())[0])\n",
    "    allprobs_q1.append((get_probs_(cir.expectation()).tolist())[1])\n",
    "    allprobs_qend.append((get_probs_(cir.expectation()).tolist())[-1])\n",
    "    allprobs_qend2.append((get_probs_(cir.expectation()).tolist())[-2])\n",
    "\n",
    "cir.draw()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "allprobs_q0 = np.matrix(allprobs_q0)\n",
    "allprobs_q1 = np.matrix(allprobs_q1)\n",
    "allprobs_qend = np.matrix(allprobs_qend)\n",
    "allprobs_qend2 = np.matrix(allprobs_qend2)\n",
    "\n",
    "fig = plt.figure(figsize=(8, 5))\n",
    "ax = fig.add_subplot(111)\n",
    "plt.xlim(0, 2*np.pi)\n",
    "plt.ylim(-0.01, 1.01)\n",
    "plt.plot(tlist, allprobs_q0[:,1], label=\"$q_0=|1>$\", color=\"dodgerblue\")\n",
    "plt.plot(tlist, allprobs_q1[:,1], label=\"$q_1=|1>$\", color=\"green\")\n",
    "plt.plot(tlist, allprobs_qend[:,1], label=\"$q_{end}=|1>$\", color=\"red\")\n",
    "plt.plot(tlist, allprobs_qend2[:,1], label=\"$q_{end-1}=|1>$\")\n",
    "plt.vlines(np.pi/2, -0.1, 1.1, ls=\"--\")\n",
    "plt.text(1.6, 0.5, \"$t=\\pi/2$\")\n",
    "plt.xlabel(\"Time\")\n",
    "plt.ylabel(\"Probability\")\n",
    "plt.xticks([0, np.pi/2, np.pi, np.pi/2*3, 2*np.pi], \n",
    "           [0, \"$\\pi/2$\", \"$\\pi$\", \"$3\\pi/2$\", \"$2\\pi$\"]\n",
    "           )\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "test",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.17"
  },
  "orig_nbformat": 4
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
